Question 81842
Going skiing, Leon drove 270 miles to the lodge in the same time as pat drove to the lodge; if pat drove 10 miles per hour faster than Leon, then how fast did each of them drive?
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Not enough information here. Need to know the distance Pat drove.
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Student responded: Pat drove 330 miles
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Let x = Leon's speed
Then (x+10) = Pat's speed
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We are told that the time is the same for both, make an equation from this:
Time = distance/speed
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Leon's time = Pat's time
{{{270/x}}} = {{{330/(x+10)}}}
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Cross multiply and you have:
330x = 270(x+10)
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330x = 270x + 2700
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330x - 270x = 2700
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60x = 2700
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x = 2700/60
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x = 45 mph is Leon's speed; then Pat's speed = 55 mph
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Check solution by seeing if the times are equal:
270/45 = 6 hrs
330/55 = 6 hrs